Rotating transformation - Calculation

Ok, i am not sure if i can transform my 9 vectors in 2… Is this correct?:
First picture vector (1,1,1) and the second picture vector (1,-1,1).
Will this get me the rotation i need?

Btw. another question: I can rotate my object around the center of my geometry with “geometry.center()”.
Is there an option to rotate the object around a point inside the object?